Third-Person Possessive Pronouns in Dual Possessives [duplicate]

Short answer

Yes, this argument does have a basis in linguistic fact, which is why some people do it in the first place, but that doesn't mean it must be correct in Standard English (and it isn't).

Longer Answer

This argument does hold water in the linguistic sense. "My wife and I" is, in fact, a phrase — a syntactic constituent. The fact that this phrase happens to end with the word I does not preclude it from taking the Saxon genitive as a whole unit. There are many cases where people apply the Saxon genitive ('s) to entire phrases in everyday speech:

1. John and Marsha's house was robbed last night.
2. I'm not a fan of 1995 to 2005's music scene at all.
3. The plants were eaten by the man next door's cat.

In the case of (1), if we follow the logic of "my wife's and my", we should have to say "John's and Marsha's house" — the genitive should have been distributed among the nouns in the conjoined phrase. Same for (2) and (3). And in (3) the 's is directly next to an adjectival phrase "next door", not even a noun phrase.

Now, people may have different opinions about which of these types of constructions they would allow and in what context; the fact is that people say these sorts of things all the time, and for most people they don't even register as anything out of the ordinary when they happen.

In Standard English, when a pronoun is involved in a conjoined phrase like "my wife and I", the genitive marker is distributed to all the noun phrases in the conjoined phrase. This would yield the construction "my wife's and my".

However, in the case of "my wife and I's", what we are seeing is one or more dialects extending this phrasal Saxon genitive to include some conjoined phrases that include pronouns. So the phrase is getting the genitive marker, rather than each of the units within the phrase.

Both approaches are linguistically sound, but only one is accepted as a standard; namely, "my wife's and my". Standard forms are chosen somewhat arbitrarily. This means that they don't have some sort of objective "correctness"; it also means that you can't argue for the correctness of a non-standard form based on logic. There are many logical ways to convey ideas, and one was chosen to be the standard. If you wish to communicate in a context where adherence to formal/standard rules is beneficial, then you should choose the standard form.

No. The apostrophe is not what makes a possessive. It marks (slightly by accident) the old genitive case -es ending, which is not the route that "I" follows.

The correct version of the noun phrase argument is "My wife and my," and it's actually the right thing to use in this particular case because it implies we are talking about a joint effort between my wife and myself. "My wife's and my" implies that each of us made separate efforts. The point is a bit moot when discussing a singular thing (the seafood collaboration dinner), but still.

The Wikipedia article on the possessive apostrophe discusses this in more depth.